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We investigate the asymmetry between electron and hole doping in a 2D Mott insulator, and the resulting competition between antiferromagnetism (AF) and d-wave superconductivity (SC), using variational Monte Carlo for projected wave functions. We find that key features of the T = 0 phase diagram, such as critical doping for SC-AF coexistence and the maximum value of the SC order parameter, are determined by a single parameter η which characterises the topology of the "Fermi surface" at half filling defined by the bare tight-binding parameters. Our results give insight into why AF wins for electron doping, while SC is dominant on the hole doped side. We also suggest using band structure engineering to control the η parameter for enhancing SC.PACS numbers: 75.10.Jm, 71.27.+a Ever since their discovery, cuprates continue to pose some of the most challenging theoretical puzzles [1] in condensed matter physics. The problem is dominated by strong electronic correlations [2,3,4, 5] and the tJ-model and its variants are believed to contain the essential physics of high T c superconductivity. In this Letter we address the following questions: What controls the electron-hole asymmetry in cuprates? Why does antiferromagnetism dominate on the electron doped side, and superconductivity on the hole doped side? How can we understand the empirical correlation between electronic structure parameters -the range of the in-plane hopping -and superconductivity, pointed out by Pavarini et al. [6]? In particular, can we get some insight into the all important question of what material parameters control the optimal SC transition temperature T max c ? Model: The minimal model that allows for an understanding of the material dependencies of the cuprate pheonomenology is the t-J model with extended hopping:where c iσ is the electron operator at site i with spin σ, n iσ = c † iσ c iσ is the density, with n i = σ n iσ , S i = 1 2 c † iα σ αβ c iβ is the spin at site i (σ's are the Pauli matrices), and J is the antiferromagnetic exchange between nearest neighbors i, j . The projection operator P = i (1 − n i↑ n i↓ ) implements the "no double occupancy" constraint.The bare dispersion has the form ǫ(k) = −2t(cos k x + cos k y ) + 4t ′ cos k x cos k y − 2t ′′ (cos 2k x + cos 2k y ) where t, t ′ and t ′′ are the nearest, second and third-neighbor hoppings respectively. The importance of t ′ and t ′′ is suggested both by ARPES experiments [7,8] and electronic structure calculations [9]. With the sign convention above, t, t ′ and t ′′ are all positive for the hole doped case. To model the electron-doped case, we make a standard particle-Thus for the electron-doped case we again obtain H witht = t,t ′ = −t ′ ,t ′′ = −t ′′ . Variational Wave function: We choose a variational ground state wave function for an N -particle system that includes both AF and SC order:The form of ϕ in the unprojected wave function is motivated by a saddle point analysis of H. For a nonzero Neel amplitude m N , we get two spin density wave (SDW) bands (α = 1, 2)′′ var...

A quantum critical point is found in the phase diagram of the two-dimensional Hubbard model [Vidhyadhiraja et al., Phys. Rev. Lett. 102, 206407 (2009)]. It is due to the vanishing of the critical temperature associated with a phase separation transition, and it separates the non-Fermi liquid region from the Fermi liquid. Near the quantum critical point, the pairing is enhanced since the real part of the bare d-wave pairing susceptibility exhibits an algebraic divergence with decreasing temperature, replacing the logarithmic divergence found in a Fermi liquid [Yang et al., Phys. Rev. Lett. 106, 047004 (2011)]. In this paper we explore the single-particle and transport properties near the quantum critical point using high quality estimates of the self energy obtained by direct analytic continuation of the self energy from Continuous-Time Quantum Monte Carlo. We focus mainly on a van Hove singularity coming from the relatively flat dispersion that crosses the Fermi level near the quantum critical filling. The flat part of the dispersion orthogonal to the antinodal direction remains pinned near the Fermi level for a range of doping that increases when we include a negative next-near-neighbor hopping t ′ in the model. For comparison, we calculate the bare d-wave pairing susceptibility for non-interacting models with the usual two-dimensional tight binding dispersion and a hypothetical quartic dispersion. We find that neither model yields a van Hove singularity that completely describes the critical algebraic behavior of the bare d-wave pairing susceptibility found in the numerical data. The resistivity, thermal conductivity, thermopower, and the Wiedemann-Franz Law are examined in the Fermi liquid, marginal Fermi liquid, and pseudo-gap doping regions. A negative next-near-neighbor hopping t ′ increases the doping region with marginal Fermi liquid character. Both T and negative t ′ are relevant variables for the quantum critical point, and both the transport and the displacement of the van Hove singularity with filling suggest that they are qualitatively similar in their effect.

A theory for the size dependence of the coefficient of thermal expansion ͑CTE͒ of nanostructures is developed. The theory predicts that the fractional change in the CTE from the bulk value scales inversely with the size of the nanostructure. An explicit relation for the intrinsic length scale that governs the size dependence is derived. The theory is tested against full-scale molecular dynamics simulations and excellent agreement is found. Further, it is shown that the CTE can rise or fall with size depending on the properties of the bounding surfaces of the nanostructure. The theory has the potential to be used as part of a predictive tool for the design of nanostructures.

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